What is the value of the natural logarithm multiplied by two?

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The discussion centers on the value of the natural logarithm multiplied by two, specifically questioning what "twice the base of the natural logarithm" means. The base of the natural logarithm is identified as e, leading to the conclusion that the expression could be interpreted as 2e. Clarification is sought on the definition of the natural logarithm being used, as it affects the outcome. If the logarithm is defined in a specific way, the result could vary significantly. Ultimately, understanding the base is crucial for determining the correct value.
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What is twice the base of the natural logarithm?
 
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acelya said:
What is twice the base of the natural logarithm?

Could you please be a little more clear? The base of the natural logarithm is e, so you could mean 2e, or possibly something else?
 
If you know what the base of the natural logarithm is, then just multiply by 2!

If you do NOT know what the base of the natural logarithm is, then what definition of "natural logarithm" are you using?
 
Acela, if it's supposed to rhyme with "chewy", then it's 2e. Otherwise it's 5.436563656918090470720574942705324995514.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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